"The argument that Constantine's Mad Russian makes is that each time
the book is borrowed he is losing royalties on a copy sold. I don't
know that there is a valid argument against this."

I can think of a few.

First, for most mid-list authors (and this includes most mystery writers), the bulk of their sales are not to individuals, but to libraries. If the libraries weren't buying their books and putting them in their collection, a significant portion of their income would be gone. The idea that private persons would buy the books if the libraries weren't making them available is flawed. Indeed, there are some publishers, like Avalon and Five Stat, that are set up primarily to provide material to libraries. If those books aren't sold to libraries, they're unlikely to get sold at all.

Second, the "library equivalent to broadcasting" analogy is flawed. When a song is broadcast, many people are hearing it simultaneously. When a book is borrowed, usually only one borrower, perhaps two, are reading it. How are you supposed to calculate a royalty on one or two readers?

Third, the library is the owner of the physical book, if not the intellectual property contained in the book, in the same sense that at individual who buys a book is the owner of the physical book, but not the intellectual property it contains. If an individual buys a book, doesn't s/he have the right to loan it to someone else? Does s/he owe the author a royalty every time s/he loans it to a friend? Why should a library?

Finally, a book's being in a library is a benefit to the author, even if it doesn't pay off in immediate royalties, because it's a permanent piece of advertising. If a borrower takes a book out of the library, and enjoys it, s/he is more likely to be on the lookout for future books by the author s/he enjoyed after being exposed to their work through the library. That's a benefit that's lost to the author if the library doesn't buy the book (as is most likely to be the case if the library has to pay a given author a royalty every time one of their books is borrowed).

Once a library (and the taxpayers who support it) are required to pay an author royalties, my guess is that you'll find libraries stocked only with books that are in the public domain. Speaking as an author, I don't think that's going to do me a lot of good.